binomial

Complimentary A-Maths Revision Class on Binomial Expansion

For Sec 4 O Level Additional Maths and IP Maths students in Singapore, looking to score full marks for Binomial Expansion

I am bringing forward my plan to return to teaching after 3 years of break.

This Friday, I'll conducting a 2 hours revision class on O Level Additional Maths.

It is an online live! lesson for Sec 4 O Level and IP. I also welcome Sec 3 to join us. As this is a revision class, the teaching pace will be faster.

Due to limited seats, priority will be given to the Sec 4 O Level and IP students.

In this 2 hours lesson, you will learn

How to score in Binomial question simply by using the given formula in the formula sheet! No memorising at all!
5 main types of questions and their respective strategies to reduce careless mistakes and get you the correct answers fast.
The very important topic linked to binomial expansion and the most common laws repeatedly use in almost every question.
Bonus: How to answer a real life binomial expansion application question on basketball games by focusing on the details instead of being stunned like the rest of your classmates.

About Me

Many of you might know me as the 10 Year Series Book Author for O Level A & E-Maths who have transformed hundreds and hundreds of students to achieve at least 4 grades jump in their exams.

I had been taking the O Level E-Maths and A-Maths exams with my students as a private candidate year after year. This got Straits Times curious and I was interviewed in "Math tutor sits exams to understand students better".

If you are looking to complete your Binomial Expansion revision within these 2 hours for your upcoming prelims, end of year exams, click on the link below to register for the complimentary online lesson.

Date: 10 July 2020, Friday (Public Holiday)
Time: 10am – 12pm
Fees: $120 $0
For: 2020 Sec 3 & 4 O Level and IP

As this is a revision lesson, Sec 3 students who want to learn this topic in advance will expect a fast teaching pace.

Webcam must be switched on when lesson is in progress.
Materials will be emailed by Thursday.

A-Math: Binomial Theorem Checklist

checklist-am Last lesson, I recapped with my students the essence of Binomial Theorem in A-Math and upon searching my website, I found that I have written quite a number of posts on this topic.

I'm going to list down the points you need to know before you go for your exams.

Do you know

How to use the Binomial formula provided on the formula sheet? (term by term expansion, (r+1)th general term, factorial formula)
What's term independent of x?
Which term to use in a double bracket expansion?
How to apply Binomial concepts in evaluating values?

Binomial theorem is closely linked to Indices and every year, there is always one question worth 5 - 7 marks in 'O' Levels.

Hope you find this post beneficial and I would love to hear your comments on Binomial theorem. Do you like this topic or you don't? Leave me a comment.

The Exclamation Mark ! in Binomial Theorem

factorial-sign-binomial Binomial Theorem came out as a 9 marks question in 2009 GCE 'O' Level Additional Mathematics Paper (Subject Code: 4038) so you know as well as I do the importance of Binomial.

Read about other useful posts on Binomial Theorems:

Binomial Expansion Teaches how to choose the RIGHT partner (:

A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method

Exam Question : Usage of Binomial Formula

I'm looking at the question now. It is testing on the usage of the Binomial formula, including the 'n choose r' formula. Many students call this sign: '!' 'exclamation mark' which is known correctly as factorial.

I will be using the following question to illustrate how to simplify the 'n choose r' formula without memorizing. (I understand some schools want students to memorize)

Let's begin by understanding what's 'n choose r' all about:

n-choose-r-binomial — Click on image for larger view

Do you know how to simplify 'n choose 3'?

Here's the question which requires us to apply what we have discussed. I would suggest you attempt it on your own before clicking here for the solution.

A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method

In the earlier post on free Math Exam Papers, we received very good response. Almost 200 copies were downloaded in less than 7 days. We have a subscriber requesting for step by step solution for the questions though we have provided the answer keys. I am sorry I am unable to provide the step by step solutions due to my busy schedule. However, subscribers can email me their workings I can assist and advice you on the incorrect workings. I hope this would be useful. Moreover, by providing the step by step solution will also not be useful as most students will perhaps take the easy way out to just "read" the solution and think that they understand them. Mastery of Mathematics is not by "reading" but it's the knowing and applying of the strategies.

I have picked up one question on Binomial Expansion (another tricky A-Math topic) for discussion. Specifically on finding Term Independent of x.

Allow me to discuss the common mistake that students make.

Most students will expand the expression term by term

Disadvantages:

Too time consuming
Higher tendency to make careless mistakes!

So the following step by step solution is what I taught my students during my A-Math Ultimate Leap Programme (For Sec 4s who still wish to join, call me @ 9685 7675. For Sec 3s, we are opening up the classes in March 2009! More info will be released in Feb. Keep reading this blog)

Features to take note:

General Term is applied (No memorization is required, just refer to the formula sheet if you aren't sure)
Constant (numbers) & variable (which is x in the question) are separated. (so that we can focus on the important part first)
Power of x is circled (in red) so that you focus all your attention on it. (Reduces careless mistakes too!)
Since this is a 4 marks question, 4 minutes is the working time to complete the solution. (Time management is part of examination techniques)

Skills required:

Understanding of Term Independent of x (i.e it's x to the power of 0 NOT x is zero!)
Usage of Binomial Formula
Basic application of Indice law (Observe that [pmath]{1}/{x^7}[/pmath] is rewritten as [pmath]x^-7[/pmath])

Evaluate the term which is independent of x in the expansion of .

So do you do your working in a similar manner or you have your own style? I would love to hear from you if you know how to do this question initially. If no, which part did you not understand?

Exam Question : Usage of Binomial Formula

Harry - a vivd reader of askalwayslovely.blogspot.com sent me an email asking about solving of the following question. He did it using trial and error. I believe it will take him some time. He felt that his approach was not the best so he emailed me asking for alternatives.

In fact for this question, there is a step by step way which will get us the answer in less than 8 minutes time.

Question: If the coefficient of [pmath]x^k[/pmath] and [pmath]x^(k+1)[/pmath] in the expansion of [pmath](2x+3)^19[/pmath] are equal, find [pmath]k[/pmath]

Click on the image for bigger view

Binomial Expansion Teaches how to choose the RIGHT partner (:

I always like to share with my students what each Math topic has to do with their everyday life, particularly their future.

Yesterday, I did Binomial Expansion. It's about finding the RIGHT partner (: It's about mastering the skills of finding the correct match based on a set of factors.

Just like this question, you see that there are 2 brackets. 1st bracket is good for now. 2nd bracket needs us to do some expansion work by using the FORMULAE (It's provided during GCE O Level Exams but some schools don't seem to provide it for their mid year, strange)
Oh yar, there is NO need to remember the Binomial Expansion Formulae!

Then one of the questions that often pop up is " When do we stop our expansion for [TEX](1+\frac {x}{3})^{12}[/TEX]?"

To answer this question, it depends on what type of partners you are looking for.